Piezoelectric Composite Laminates Research Articles

Fractional-Order Rate-Dependent Piezoelectric Thermoelasticity Theory Based on New Fractional Derivatives and its Application in Structural Transient Response Analysis of Smart Piezoelectric Composite Laminates

Ultrafast heating technology (e.g., high-energy pulse-burst laser, laser-aided material processing, etc.) has been extensively used in micro-machining and manufacturing of piezoelectric devices (e.g., piezoelectric resonator, piezoelectric generators, etc.), and the related thermo-electromechanical coupling analysis becomes more significantly important. In recent years, although rate-dependent piezoelectric thermoelasticity theories were historically proposed, the memory-dependence feature of strain relaxation and heat conduction has not been considered yet. In this work, the unified forms of fractional order strain and heat conduction are developed by adopting fractional derivatives of the Caputo (C), Caputo–Fabrizio (CF), Atangana–Baleanu (AB), and Tempered–Caputo (TC) types. Following these models, a fractional-order rate-dependent piezoelectric thermoelasticity is established. With the aid of an extended thermodynamics framework, the new constitutive and governing equations are derived. The proposed theory is applied to investigate dynamic thermo-electromechanical responses of smart piezoelectric composite laminates with imperfect interfacial conditions by the Laplace transformation approach. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on wave propagations and structural thermo-electromechanical responses are evaluated and discussed in detail.

Integrated a nonlinear energy sink and a piezoelectric energy harvester using simply-supported bi-stable piezoelectric composite laminate

A nonlinear device is presented for simultaneous vibration absorption and energy harvesting. This device is composed of a nonlinear energy sink and a piezoelectric energy harvester (NES-EH), and its core component is the simply-supported bi-stable piezoelectric composite laminate (BPCL). Its outstanding advantages are light weight, simple and reliable structure. The theoretical model is developed to model a harmonically excited linear oscillator coupled with NES-EH. The Runge–Kutta method and the harmonic balance method (HBM) are used to solve the theoretical model numerically and analytically. The vibration suppression efficiency is utilized to quantify the vibration absorption performance, while the energy harvesting performance is assessed by bandwidth for energy harvesting and maximum voltage within the bandwidth. The effects of the excitation amplitude, the concentrated mass of NES-EH, the length and width of BPCL, and the load resistance are considered on the performances of NES-EH. The vibration absorption and energy harvesting performances of NES-EH can be improved by adjusting these parameters. In addition, the proposed NES-EH can achieve the goal of higher power density and normalized power density under low-amplitude excitation and simultaneously have a good vibration absorption effect. Finally, approximate analytical solutions are obtained by using HBM to exhibit various bifurcations and singularities.

The dynamic regimes and the energy harvesting of the energy harvester based on the bistable piezoelectric composite laminate

The dynamic regimes and the energy harvesting of the bistable energy harvester based on the bistable piezoelectric composite laminate are elaborated here. To identify the all-around dynamic regimes and assess the bistable energy harvesting performance, the forward frequency sweep, the reverse frequency sweep and the resistance sweep are conducted. The peak-to-peak frequency–amplitude response curves on the displacement and the voltage output are graphically presented. The single-well vibration, the limit cycle oscillations, the intermittency between the limit cycle oscillations and the chaotic snapthrough, the intermittency between the multiple periods snapthrough and the chaotic snapthrough, the multiple periods snapthrough and the chaotic snapthrough are elaborated by the Time history diagram, the Phase diagram and the Poincare map. The dynamic regimes are graphically presented delivering the stability zone for the dynamic responses and the optimal region for the energy harvesting. The RMS power output and the Max voltage output are checked to be the value judgements. Due to the softening nonlinear effect and the hysteresis, the conspicuous biases between the forward and reverse frequency sweeps are found to exist illustrating that the limit cycle oscillations expand the bandwidth of the double-well regimes during the reverse frequency sweep. From the perspective of the energy harvesting capacity, the limit cycle oscillations are demonstrated to be optimal, the double-well responses generally outperform the single-well responses concerning the off-resonance and the single-well responses concerning the primary resonance around the reduced modal frequency may outperform the double-well responses except the limit cycle oscillations. The load resistance is crucial to the power generation performance and needs optimizing with the change of the external excitation. The load resistance, the external excitation amplitude and frequency are interrelated and can be optimized simultaneously for the maximum power generation efficiency.

Electrospun Polyvinylidene Fluoride Piezoelectric Fiber Glass/Carbon Hybrid Self-Sensing Composites for Structural Health Monitoring.

In this study, a polyvinylidene fluoride (PVDF)/graphene nanoplatelet (GNP) micro-nanocomposite membrane was fabricated through electrospinning technology and was employed in the fabrication of a fiber-reinforced polymer composite laminate. Some glass fibers were replaced with carbon fibers to serve as electrodes in the sensing layer, and the PVDF/GNP micro-nanocomposite membrane was embedded in the laminate to confer multifunctional piezoelectric self-sensing ability. The self-sensing composite laminate has both favorable mechanical properties and sensing ability. The effects of different concentrations of modified multiwalled carbon nanotubes (CNTs) and GNPs on the morphology of PVDF fibers and the β-phase content of the membrane were investigated. PVDF fibers containing 0.05% GNPs were the most stable and had the highest relative β-phase content; these fibers were embedded in glass fiber fabric to prepare the piezoelectric self-sensing composite laminate. To test the laminate's practical application, four-point bending and low-velocity impact tests were performed. The results revealed that when damage occurred during bending, the piezoelectric response changed, confirming that the piezoelectric self-sensing composite laminate has preliminary sensing performance. The low-velocity impact experiment revealed the effect of impact energy on sensing performance.

A bi-stable device for simultaneous vibration absorption and energy harvesting using bi-stable piezoelectric composite laminate

A bi-stable device is presented for simultaneous vibration absorption and energy harvesting by introducing the piezoelectric element into the bi-stable nonlinear energy sink (BNES), which is called the bi-stable piezoelectric absorber (BPZA). BPZA only consists of the cantilever bi-stable piezoelectric composite laminate (BPCL) and tip masses. This BPZA is a lightweight, simple and reliable structure since it does not need any external devices to maintain bistability. A finite element model (FEM) and an equivalent theoretical model are developed to model a harmonically excited linear oscillator coupled with BPZA. The Runge-Kutta method is used to solve the theoretical model numerically. The effects of the excitation amplitude, the tip mass of BPZA and the load resistance are considered on the vibration suppression efficiency and energy harvesting of BPZA. The results show adjusting these parameters can improve the vibration suppression efficiency and energy harvesting of BPZA. In addition, the experimental prototype is prepared and verifies the rightness of the finite element model and theoretical model. The BPZA achieves the goal of higher power density at lower acceleration and simultaneously has a good vibration absorption effect. Maximum power of 15.8mW is generated at an excitation frequency of 22 Hz and acceleration of 0.5 g.

Analytical modeling of panel flutter and active control in supersonic variable stiffness composite laminates

This work focuses on panel flutter and active control in supersonic variable stiffness composite laminates, making progress on the analytical modeling and combined exploration of curvilinear fiber composites tailoring and piezoelectric sensors/actuators, as promising structural design technologies, for aeroelastic control. The Classical Laminated Plate Theory and the First-Order Piston Theory are used as structural and aerodynamic models, respectively. Flutter analyses are carried out for simply supported plates, either purely elastic laminates or piezoelectric composite laminates. The tailor-ability of curvilinear fiber composites and the effect of proportional control are discussed. Ultimately, the presented results provide a comprehensive benchmark for future assessments.

On the design of a piezoelectric self-sensing smart composite laminate

The structural health monitoring of composite laminates is a rapidly emerging need in structural applications. Different real-time sensors integrated into laminates have been proposed, such as fiber Bragg gratings and piezoceramics. However, their presence negatively affects the mechanical properties of the hosting laminate.This work proposes a non-invasive method for piezoelectric functionalization of composite laminates by interleaving lead zirconate titanate micrometric powder between glass-fiber-reinforced polymer plies. The effects of different powder volume fractions on the electromechanical properties were evaluated in terms of the electrical response and laminate inherent strength. The lead zirconate titanate powder laminates demonstrated an electrical sensitivity value that was up to 439% higher compared with that of the embedded commercial disk laminate (12.4 V/kN versus 2.3 V/kN). Impact tests revealed that the resistance of the interleaved lead zirconate titanate powder laminates is comparable to that of the pristine laminates, whereas a fragile commercial disk leads to delamination. Furthermore, an analytical model was proposed to predict the piezoelectric voltage coefficient g33 as a function of the electrical properties, volumetric powder fractions, and polarization process. The model matched the experimental g33 coefficients (R2=0.97), demonstrating its capability to predict the electromechanical behavior of piezoelectric composites and define their design guidelines.

Piezoelasticity solution for edge stress field in weakly bonded piezoelectric composite laminates

The delamination/debonding failure in laminated structures is often caused by development of concentrated stress fields near the edges. Because of their three-dimensional (3D) nature, it is important to develop accurate elasticity solutions for these fields, which should include the possibility of non-rigid layer interfaces, to have realistic predictions. This article presents an accurate 3D piezoelasticity-based analytical solution for smart composite panels featured with piezoelectric sensor/actuator layers, having interfacial bonding imperfections and showing edge effects. The displacement and electric field discontinuities at the imperfectly bonded layer interfaces are represented by adopting the generalized spring–layer model. The model is implemented into the Reissner-type mixed variational principle for the piezoelectric medium. The partial differential equations thus developed are solved using the mixed-field multiterm Kantorovich method, which exactly satisfy all the mechanical and electric boundary conditions at the panel edges, top and bottom surfaces of the panel and interlaminar continuity/jump conditions. The accuracy and convergence of the present results are established in comparison with the available exact piezoelasticity solutions for simply supported panels. The effect of compliance and imperfection location on the electromechanical response of piezolaminated composite panels with edge effects is investigated. The influence of actuator debonding on the interlaminar stress transfer and actuation authority is also shown.

Evaluation of exact electro-elastic static and free vibration solutions of multilayered plates for benchmarking: Piezoelectric composite laminates and soft core sandwich plates

This work provides a study on three-dimensional exact electro-elastic static and free vibration solutions of multilayered plates, focused on a comprehensive evaluation of well-known benchmarks for piezoelectric and/or composite laminates as well as soft core sandwich plates, adding much to thus far available in the literature. The exact solution method for simply supported multilayered plates is fully described in line with earlier leading works, compiled in a single study in a consistent form throughout. The layers involved can be either piezoelectric layers poled through-thickness (i.e. extension mode) or purely elastic layers, including composite layers. For each layer, the form of the through-thickness exact solution depends strongly on its material properties, thus each case arising from an orthotropic, transversely isotropic or simply isotropic layer is considered specifically. Within the free vibration solution, in agreement with an in-plane mode (nx, ny), the so-called special modes for either nx=0 or ny=0, though often overlooked, are purposely addressed, along with thickness modes for each pair (nx, ny). The benchmarks cover purely elastic solutions, as in composite laminates and soft core sandwich plates, as well as electro-elastic solutions, namely piezoelectric composite laminates, involving not only but especially thick plates. For each multilayered plate, the static solution considers either an applied load or an applied electric potential, providing a detailed through-thickness evaluation of displacements and stresses, and when present, the electric potential and electric displacements. The respective free vibration solution reveals the first twenty natural frequencies and associated modes, including all together special modes and thickness modes.

Improvement of the band-gap characteristics of active composite laminate metamaterial plates

The characteristics of vibration frequency band-gaps for the composite laminate metamaterial plates are improved by equidistantly placing macro-fiber composite (MFC) piezoelectric patches along one direction of the plates. An acceleration feedback control strategy is proposed to actively regulate the band-gap characteristics of the metamaterial plates. The spectral element method (SEM) and transfer matrix method are used to calculate frequency response curves and attenuation constants of the metamaterial plates, and the calculated results by the SEM are compared with that of the finite element method (FEM) to validate the correctness and accuracy of the present numerical method. The obtained results demonstrate that when lattice constant of the structure is properly designed, superior band-gap properties in the low and medium frequency ranges can be achieved by adjusting the dimensions of the MFC piezoelectric patches. Improved characteristics of the Bragg scattering band-gaps in the medium and high frequency regions can also be obtained using the acceleration feedback control strategy. Moreover, band-gap widths can be significantly enlarged by actively tuning the acceleration feedback gain. In addition, the starting frequencies and band-gap widths of the composite laminate metamaterial plates can be adjusted using different cross-ply angles of the MFC piezoelectric patches and composite laminate metamaterial plates.

A comprehensive electromechanically coupled model for non-uniform piezoelectric energy harvesting composite laminates

Achieving high power densities through initiative designs of piezoelectric harvester in various geometries is a key point in vibration energy harvesting. State-of-the-art analytical and finite element models (FEMs) ignore structural damping, inter-laminar continuity, shear stresses, and contact layer effect between the substrate and piezoelectric layers and in addition cannot predict the performance of many recently introduced piezoelectric harvester configurations, such as non-uniform, thick piezoelectric patches, and variable thickness beams. This paper presents a comprehensive finite element formulation to calculate power generation by piezoelectric harvesters in a broader range of design cases. The presented high-order shear FEM not only is suitable for thick composite-based harvesters but also accommodates the drawbacks of the previous methods. The coupled finite element approach is verified versus experimental and analytical results. The model developed in this work is employed to analyze a non-uniform energy harvester with an E-glass fiber composite substrate layer sandwiched between piezoelectric layers with variable thickness. The numerical results show that, the advance formulation is capable of analyzing various piezoelectric harvesters including various influential parameters such as contact layer and damping dissipation. The results, furthermore, indicate that variable piezoelectric-layer thickness and an optimum fiber direction in composite substrate lamina can enhance performance of the piezoelectric harvester.

Micromechanical RVE model application for generalization of smart composite laminate structures with thermoelastic characteristics

A generalization of the piezoelectric composite laminate plate model is investigated. To avoid depending on experimentally determined moduli, a micromechanical model based on the Reduced Volume Element (RVE) was used to calculate the effective moduli of the composite. This study applies the finite element method (FEM) based on the First-order Shear Deformation Theory of Plates (FSDTP). To validate the accuracy of the model, the overall deflection under various loads, voltages, temperatures, and dynamic pressures are calculated with both mechanical moduli. Nonlinear analysis is performed through the Newton-Raphson Iterative method. Furthermore, the active control of the plate with the piezoelectric layers is presented through the transient response using the Newmark method. In all cases, the micromechanical model was in good agreement with the experimental model. Also, an improved shear correction factor (SCF) was implemented to allow for further generalizations in the context of composite plate structures. The factors are shown with various ply-angles of the composite layer. Additionally, the application of Macro-Fiber Composites (MFC) piezoelectric layers instead of isotropic piezoelectric layers is investigated.

Design and analysis of a broadband vibratory energy harvester using bi-stable piezoelectric composite laminate

In this paper, a bi-stable piezoelectric energy harvester based on the bi-stable hybrid composite laminate with a new stacking sequence design is proposed. The new stacking sequence enables this bi-stable energy harvester to have some unique features, such as uniform strains of piezoelectric elements and symmetric stable configurations. Meanwhile, the new stacking sequence design enhances the room to adjust its natural frequency such that this proposed harvester allows for adjusting to lower frequency range and increasing the inertia by a tip mass to lower the demand of excitation level in comparison to previous settings. A finite element analysis is developed to investigate the static and dynamic characteristics of this new bi-stable energy harvester. A simple numerical model with a modified version of the Duffing equation is developed based on the unique nonlinear restoring force obtained from finite element analysis to describe the fundamental response characteristics of this nonlinear bi-stable energy harvester. Numerical simulations and experiments are carried out at different harmonic excitation levels ranging from 10 to 40 Hz. The results verify that the proposed model can reasonably capture the dynamic characteristics of this broadband bi-stable energy harvester. The output powers were measured under different vibration patterns. Maximum power of 31.1 mW was generated under large-amplitude and high-energy orbits cross-well vibration pattern at an excitation frequency of 22 Hz and acceleration of 3g (g = 9.8 m/s2).

Linear shell elements for active piezoelectric laminates

Piezoelectric composite laminates are a powerful material system that offers vast options to improve structural behavior. Successful design of piezoelectric adaptive structures and testing of control laws call for highly accurate, reliable and numerically efficient numerical tools. This paper puts focus onto linear and geometrically nonlinear static and dynamic analysis of smart structures made of such a material system. For this purpose, highly efficient linear 3-node and 4-node finite shell elements are proposed. Both elements employ the Mindlin-Reissner kinematics. The shear locking effect is treated by the discrete shear gap (DSG) technique with the 3-node element and by the assumed natural strain (ANS) approach with the 4-node element. Geometrically nonlinear effects are considered using the co-rotational approach. Static and dynamic examples involving actuator and sensor function of piezoelectric layers are considered.

Computational model for supporting SHM systems design: Damage identification via numerical analyses

This work presents a computational model to simulate thin structures monitored by piezoelectric sensors in order to support the design of SHM systems, which use vibration based methods. Thus, a new shell finite element model was proposed and implemented via a User ELement subroutine (UEL) into the commercial package ABAQUS™. This model was based on a modified First Order Shear Theory (FOST) for piezoelectric composite laminates. After that, damaged cantilever beams with two piezoelectric sensors in different positions were investigated by using experimental analyses and the proposed computational model. A maximum difference in the magnitude of the FRFs between numerical and experimental analyses of 7.45% was found near the resonance regions. For damage identification, different levels of damage severity were evaluated by seven damage metrics, including one proposed by the present authors. Numerical and experimental damage metrics values were compared, showing a good correlation in terms of tendency. Finally, based on comparisons of numerical and experimental results, it is shown a discussion about the potentials and limitations of the proposed computational model to be used for supporting SHM systems design.

A refined theory with exponential through-thickness approximation for cross-ply piezoelectric composite laminates with weak interfaces

An equivalent single layer theory for piezoelectric composite laminates with weak interfaces is built by deducing three through-thickness functions in displacement and potential fields from the three-dimensional elasticity equilibrium equations and electrostatics charge equation. It uses exponential approximation through thickness in displacements and potential. The interfacial bonding conditions are characterized by a linear slip law and an electrically semi-permeable assumption, and used to determine the three through-thickness functions. This refined theory shows high accuracy, but use only six displacement and potential variables, the number of which is independent of the number of layers involved. The closed-form solutions of piezoelectric laminates in cylindrical bending subjected to different sets of edge boundary conditions are presented and fill the gaps in literature. The present solutions can predicts the singular effects of stresses near clamped edges.

Erratum to: Piezothermoelastic responses of piezoelectric composite laminates with weak interfaces

Erratum to: Piezothermoelastic responses of piezoelectric composite laminates with weak interfaces

Piezothermoelastic responses of piezoelectric composite laminates with weak interfaces

Interfacial weak bonding affects piezothermoelastic responses of piezoelectric composite laminates. To simplify the complicated piezothermoelastic constitutive laws at a weak interface, three assumptions on interfacial bonding conditions are made. They are (i) the relations between the interfacial displacement jumps and the interfacial transverse stresses; (ii) the relation (electrically semi-permeable assumption) between the interfacial potential jump and the interfacial normal electric displacement; (iii) the relation between the interfacial temperature jump and the interfacial normal opening. These assumptions form a set of systematic descriptions of three-fields-coupling at a weak interface and result in a linear mathematical formulation. The piezothermoelastic solutions of cross-ply piezoelectric laminates with weak interfaces in cylindrical bending are deduced. Some benchmark numerical results are obtained, and the effects of interfacial weak bonding on the piezothermoelastic responses are discussed.

Three-dimensional analysis for rectangular 1–3 piezoelectric fiber-reinforced composite laminates with the interdigitated: electrodes under electromechanical loadings

In this paper, an exact analysis for the rectangular composite laminated plate consisting of 1–3 piezoelectric fiber-reinforced composite layer and orthotropic elastic composite layer subjected to the electric field with the interdigitated electrode (IDE) and arbitrary loads is presented without any simplification. The solution of the derived governing differential equations is obtained through the power series expansion and Fourier expansion methods. An illustrative analysis is carried out to investigate the influence of the stiffness anisotropy, free-strain anisotropy and electric field on the shear curvature of the laminated plate with 1–3 active fiber-reinforced composite layer. The numerical results show that, the magnitude of shear curvature gradually increases as the stiffness anisotropy and the free-strain anisotropy increase, and increasing the electrical field also leads to an increase in shear curvature. Results presented here can be used to assess various approximate theories and enhance the understanding of the static and dynamic response behavior of the 1–3 piezoelectric composite structures.

Modelling of cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip

An approximate theory for cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip is developed. This theory uses only 4 displacement and potential variables, the number of which is independent of the number of layers involved. The displacement and electric potential fields are depicted by the displacement and electric potential distribution functions through thickness, respectively. The two functions are formulated according to particular solutions to the three-dimensional elasticity equilibrium equations and electrostatics charge equation. In this shear slip modelling interfacial opening is neglected. The interfacial bonding conditions are characterised by a linear slip law and an electrically permeable assumption. A corresponding finite element is also developed to deal with piezoelectric laminates with local shear slip. The accuracy and effectiveness of the present theory are demonstrated in numerical examples.